Multiblock principal component analysis with instrumental variables

Function to perform a multiblock redundancy analysis of several explanatory blocks $(X_1, \dots, X_k)$, defined as an object of class ktab, to explain a dependent dataset $Y$, defined as an object of class dudi

Usage

mbpcaiv(dudiY, ktabX, scale = TRUE, option = c("uniform", "none"), scannf = TRUE, nf = 2)

Arguments

dudiY: an object of class dudi containing the dependent variables
ktabX: an object of class ktab containing the blocks of explanatory variables
scale: logical value indicating whether the explanatory variables should be standardized
option: an option for the block weighting. If uniform, the block weight is equal to $1/K$ for $(X_1, \dots, X_K)$ and to $1$ for $X$ and $Y$. If none, the block weight is equal to the block inertia
scannf: logical value indicating whether the eigenvalues bar plot should be displayed
nf: integer indicating the number of kept dimensions

Value

A list containing the following components is returned:

call: the matching call
tabY: data frame of dependent variables centered, eventually scaled (if scale=TRUE) and weighted (if option="uniform")
tabX: data frame of explanatory variables centered, eventually scaled (if scale=TRUE) and weighted (if option="uniform")
TL, TC: data frame useful to manage graphical outputs
nf: numeric value indicating the number of kept dimensions
lw: numeric vector of row weights
X.cw: numeric vector of column weighs for the explanalatory dataset
blo: vector of the numbers of variables in each explanatory dataset
rank: maximum rank of the analysis
eig: numeric vector containing the eigenvalues
lX: matrix of the global components associated with the whole explanatory dataset (scores of the individuals)
lY: matrix of the components associated with the dependent dataset
Yc1: matrix of the variable loadings associated with the dependent dataset
Tli: matrix containing the partial components associated with each explanatory dataset
Tl1: matrix containing the normalized partial components associated with each explanatory dataset
Tfa: matrix containing the partial loadings associated with each explanatory dataset
cov2: squared covariance between lY and Tl1
Yco: matrix of the regression coefficients of the dependent dataset onto the global components
faX: matrix of the regression coefficients of the whole explanatory dataset onto the global components
XYcoef: list of matrices of the regression coefficients of the whole explanatory dataset onto the dependent dataset
bip: block importances for a given dimension
bipc: cumulated block importances for a given number of dimensions
vip: variable importances for a given dimension
vipc: cumulated variable importances for a given number of dimensions

References

Bougeard, S., Qannari, E.M. and Rose, N. (2011) Multiblock Redundancy Analysis: interpretation tools and application in epidemiology. Journal of Chemometrics, 23, 1-9

Bougeard, S. and Dray S. (2018) Supervised Multiblock Analysis in R with the ade4 Package. Journal of Statistical Software, 86 (1), 1-17. doi:10.18637/jss.v086.i01

Author

Stéphanie Bougeard (stephanie.bougeard@anses.fr) and Stéphane Dray (stephane.dray@univ-lyon1.fr)

Examples

data(chickenk)
Mortality <- chickenk[[1]]
dudiY.chick <- dudi.pca(Mortality, center = TRUE, scale = TRUE, scannf =
FALSE)
ktabX.chick <- ktab.list.df(chickenk[2:5])
resmbpcaiv.chick <- mbpcaiv(dudiY.chick, ktabX.chick, scale = TRUE,
option = "uniform", scannf = FALSE)
summary(resmbpcaiv.chick)
#> Multiblock principal component analysis with instrumental variables
#> 
#> Class: multiblock mbpcaiv
#> Call: mbpcaiv(dudiY = dudiY.chick, ktabX = ktabX.chick, scale = TRUE, 
#>     option = "uniform", scannf = FALSE)
#> 
#> Total inertia: 125.8
#> 
#> Eigenvalues:
#>     Ax1     Ax2     Ax3     Ax4     Ax5 
#>  44.144  26.332  23.758  19.672   5.364 
#> 
#> Projected inertia (%):
#>     Ax1     Ax2     Ax3     Ax4     Ax5 
#>  35.103  20.939  18.893  15.643   4.265 
#> 
#> Cumulative projected inertia (%):
#>     Ax1   Ax1:2   Ax1:3   Ax1:4   Ax1:5 
#>   35.10   56.04   74.93   90.58   94.84 
#> 
#> (Only 5 dimensions (out of 20) are shown)
#> 
#> Inertia explained by the global latent, i.e., resmbpcaiv.chick$lX (in %): 
#> 
#> dudiY.chick$tab and ktabX.chick: 
#>     varY varYcum varX varXcum
#> Ax1 41.2    41.2 6.94    6.94
#> Ax2 21.5    62.7 7.31   14.25
#> 
#> FarmStructure:
#>     varXk varXkcum
#> Ax1  4.68     4.68
#> Ax2  5.02     9.70
#> 
#> OnFarmHistory:
#>     varXk varXkcum
#> Ax1  6.81     6.81
#> Ax2  9.10    15.91
#> 
#> FlockCharacteristics:
#>     varXk varXkcum
#> Ax1 12.38     12.4
#> Ax2  4.13     16.5
#> 
#> CatchingTranspSlaught:
#>     varXk varXkcum
#> Ax1  3.88     3.88
#> Ax2 11.01    14.88
if(adegraphicsLoaded())
plot(resmbpcaiv.chick)